# Fluctuations in percolation of sparse complex networks

## TL;DR

This paper investigates how fluctuations affect percolation in sparse complex networks, introducing a message-passing framework and analytical tools to predict network robustness under damage, with applications to ecological and infrastructure systems.

## Contribution

It presents a novel message-passing algorithm and analytical approach to quantify fluctuations in percolation of sparse networks, including correlated damage scenarios.

## Key findings

- The framework accurately predicts fluctuations in real ecological networks.
- It characterizes the response variability of infrastructure networks to damage.
- The approach extends understanding of network resilience beyond average behavior.

## Abstract

We study the role of fluctuations in percolation of sparse complex networks. To this end we consider two random correlated realizations of the initial damage of the nodes and we evaluate the fraction of nodes that are expected to remain in the giant component of the network in both cases or just in one case. Our framework includes a message-passing algorithm able to predict the fluctuations in a single network, and an analytic prediction of the expected fluctuations in ensembles of sparse networks. This approach is applied to real ecological and infrastructure networks and it is shown to characterize the expected fluctuations in their response to external damage.